Importing the neccessary libraries and data

# Libraries to help with reading and manipulating data
import numpy as np
import pandas as pd

# Libraries to help with data visualization
import matplotlib.pyplot as plt
import seaborn as sns

sns.set()

# Removes the limit for the number of displayed columns
pd.set_option("display.max_columns", None)
# Sets the limit for the number of displayed rows
pd.set_option("display.max_rows", 200)

from sklearn.linear_model import LinearRegression
from sklearn.metrics import mean_squared_error
import statsmodels.api as sm
from statsmodels.regression.linear_model import OLS

Import the data

df = pd.read_csv("used_phone_data.csv")

Data Overview

df.head()

	brand_name	os	screen_size	4g	5g	main_camera_mp	selfie_camera_mp	int_memory	ram	battery	weight	release_year	days_used	new_price	used_price
0	Honor	Android	23.97	yes	no	13.0	5.0	64.0	3.0	3020.0	146.0	2020	127	111.62	86.96
1	Honor	Android	28.10	yes	yes	13.0	16.0	128.0	8.0	4300.0	213.0	2020	325	249.39	161.49
2	Honor	Android	24.29	yes	yes	13.0	8.0	128.0	8.0	4200.0	213.0	2020	162	359.47	268.55
3	Honor	Android	26.04	yes	yes	13.0	8.0	64.0	6.0	7250.0	480.0	2020	345	278.93	180.23
4	Honor	Android	15.72	yes	no	13.0	8.0	64.0	3.0	5000.0	185.0	2020	293	140.87	103.80

df.describe()

	screen_size	main_camera_mp	selfie_camera_mp	int_memory	ram	battery	weight	release_year	days_used	new_price	used_price
count	3571.000000	3391.000000	3569.000000	3561.000000	3561.000000	3565.000000	3564.000000	3571.000000	3571.000000	3571.000000	3571.000000
mean	14.803892	9.400454	6.547352	54.532607	4.056962	3067.225666	179.424285	2015.964996	675.391487	237.389037	109.880277
std	5.153092	4.818396	6.879359	84.696246	1.391844	1364.206665	90.280856	2.291784	248.640972	197.545581	121.501226
min	2.700000	0.080000	0.300000	0.005000	0.030000	80.000000	23.000000	2013.000000	91.000000	9.130000	2.510000
25%	12.700000	5.000000	2.000000	16.000000	4.000000	2100.000000	140.000000	2014.000000	536.000000	120.130000	45.205000
50%	13.490000	8.000000	5.000000	32.000000	4.000000	3000.000000	159.000000	2016.000000	690.000000	189.800000	75.530000
75%	16.510000	13.000000	8.000000	64.000000	4.000000	4000.000000	184.000000	2018.000000	872.000000	291.935000	126.000000
max	46.360000	48.000000	32.000000	1024.000000	16.000000	12000.000000	950.000000	2020.000000	1094.000000	2560.200000	1916.540000

print(f"The Shape of the dataframe is {df.shape[0]} rows and {df.shape[1]} columns.")  # f-string

The Shape of the dataframe is 3571 rows and 15 columns.

df.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 3571 entries, 0 to 3570
Data columns (total 15 columns):
 #   Column            Non-Null Count  Dtype  
---  ------            --------------  -----  
 0   brand_name        3571 non-null   object 
 1   os                3571 non-null   object 
 2   screen_size       3571 non-null   float64
 3   4g                3571 non-null   object 
 4   5g                3571 non-null   object 
 5   main_camera_mp    3391 non-null   float64
 6   selfie_camera_mp  3569 non-null   float64
 7   int_memory        3561 non-null   float64
 8   ram               3561 non-null   float64
 9   battery           3565 non-null   float64
 10  weight            3564 non-null   float64
 11  release_year      3571 non-null   int64  
 12  days_used         3571 non-null   int64  
 13  new_price         3571 non-null   float64
 14  used_price        3571 non-null   float64
dtypes: float64(9), int64(2), object(4)
memory usage: 418.6+ KB

Automated EDA

import sys
!{sys.executable} -m pip install pandas-profiling

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import pandas_profiling

pandas_profiling.ProfileReport(df)

Transform Object Data into Categorical Data

df['brand_name'] = df['brand_name'].astype('category')

df['os'] = df['os'].astype('category')

df['4g'] = df['4g'].astype('category')

df['5g'] = df['5g'].astype('category')

df.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 3571 entries, 0 to 3570
Data columns (total 15 columns):
 #   Column            Non-Null Count  Dtype   
---  ------            --------------  -----   
 0   brand_name        3571 non-null   category
 1   os                3571 non-null   category
 2   screen_size       3571 non-null   float64 
 3   4g                3571 non-null   category
 4   5g                3571 non-null   category
 5   main_camera_mp    3391 non-null   float64 
 6   selfie_camera_mp  3569 non-null   float64 
 7   int_memory        3561 non-null   float64 
 8   ram               3561 non-null   float64 
 9   battery           3565 non-null   float64 
 10  weight            3564 non-null   float64 
 11  release_year      3571 non-null   int64   
 12  days_used         3571 non-null   int64   
 13  new_price         3571 non-null   float64 
 14  used_price        3571 non-null   float64 
dtypes: category(4), float64(9), int64(2)
memory usage: 322.7 KB

Conduct Manual EDA

sns.pairplot(df)

<seaborn.axisgrid.PairGrid at 0x2088603de80>

df_attr = df.iloc[:, 0:16]
sns.pairplot(df_attr, diag_kind='kde')

<seaborn.axisgrid.PairGrid at 0x2089a1227f0>

fig, ax = plt.subplots(figsize = (15,15))
a = sns.boxplot(x= "os", y = 'used_price' , data = df, hue = 'brand_name')
plt.show()

fig, ax = plt.subplots(figsize = (15,15))
a = sns.boxplot(x= "os", y = 'used_price' , data = df)
plt.show()

fig, ax = plt.subplots(figsize = (15,15))
a = sns.boxplot(x= "os", y = 'used_price' , data = df)
plt.show()

New and Used Price appear to contain a significant amount of outliers

# let's plot all the columns to look at their distributions

for i in df.columns:
    plt.figure(figsize=(7, 4))
    sns.histplot(data=df, x=i)
    plt.show()

# let's plot the scatterplots of median price with all the features

for i in df.columns:
    plt.figure(figsize=(6, 6))
    sns.scatterplot(data=df, x=i, y="used_price")
    plt.show()

# let's plot the scatterplots of median price with all the features

for i in df.columns:
    plt.figure(figsize=(6, 6))
    sns.scatterplot(data=df, x=i, y="used_price")
    plt.show()

Identify Outliers

quartiles = np.quantile(df['used_price'][df['used_price'].notnull()], [.25, .75])
power_4iqr = 4 * (quartiles[1] - quartiles[0])
print(f'Q1 = {quartiles[0]}, Q3 = {quartiles[1]}, 4*IQR = {power_4iqr}')
outlier_used_price = df.loc[np.abs(df['used_price'] - df['used_price'].median()) > power_4iqr, 'used_price']
outlier_used_price

Q1 = 45.205, Q3 = 126.0, 4*IQR = 323.18

35      1049.97
37       413.14
45      1185.73
47       418.28
80       565.13
81       524.45
85       715.20
111      901.27
122      559.03
123      490.04
124      400.43
125      568.56
137      571.38
141      585.46
148      503.47
161      470.69
165      472.89
175      510.57
176      417.14
204     1248.99
210      448.34
216      533.34
260     1049.06
262      413.81
270      850.85
271      464.79
272      414.68
305      655.75
306      524.51
310      550.27
336      894.04
347      553.77
348      489.18
349      553.59
350      400.00
362      655.93
366      450.34
377      611.78
378      518.80
379      663.74
382      822.39
387      460.58
401      749.84
402      600.80
404      551.54
666      550.40
667      439.68
668      625.06
669      460.16
674      399.51
677      725.96
680      450.35
683      749.79
684      435.14
697      424.88
740      474.64
853      400.30
974      450.12
1044     583.07
1086     459.84
1131     479.52
1132     425.16
1208     423.64
1306     440.32
1307     443.76
1313    1150.41
1325    1039.60
1326     400.40
1341     520.10
1354     479.72
1696     617.09
1697     404.68
1699     401.07
1710     422.99
2110     431.78
2225     540.90
2445     726.73
2448     875.62
2454     453.34
2759     418.29
2779     650.33
2785     449.43
3032     400.24
3305     475.70
3317     550.33
3320    1916.54
3325     476.44
3326     597.26
3334     427.50
3337     412.08
3366     699.64
3367     613.87
3387     698.61
3394     407.09
3418     436.77
3420     535.92
3448     448.26
3460     548.87
3463    1916.34
3468     505.86
3469     597.14
3477     490.54
3478     540.01
3480     451.07
3509     702.85
3510     566.32
3511     439.92
3536     667.92
3537     789.54
3538     533.07
3539     495.89
3540     506.96
3541     453.12
3542     597.10
3552     765.02
3553     598.02
3562     592.09
3563     535.75
3564     401.39
3565     756.99
3566     490.96
Name: used_price, dtype: float64

quartiles = np.quantile(df['new_price'][df['new_price'].notnull()], [.25, .75])
power_4iqr = 4 * (quartiles[1] - quartiles[0])
print(f'Q1 = {quartiles[0]}, Q3 = {quartiles[1]}, 4*IQR = {power_4iqr}')
outlier_new_price = df.loc[np.abs(df['new_price'] - df['new_price'].median()) > power_4iqr, 'new_price']
outlier_new_price

Q1 = 120.13, Q3 = 291.935, 4*IQR = 687.22

35      1399.9900
45      1699.3600
85      1100.1200
111     1200.8500
137      880.8000
141      900.8700
204     2498.2400
260     1398.4700
270     1701.5400
310     1100.3100
336     1197.4900
362      879.7600
366      900.5800
377      880.7100
379     1020.0400
382     1100.6200
401      999.5800
407      879.7200
666     1100.8600
667      879.1000
668     1250.3200
669     1150.3200
674      999.0000
677     1451.9200
680      900.6300
683     1499.0700
684     1449.8200
740      949.2700
853     1000.4900
974      899.9500
1044     899.4100
1086    1149.6400
1131     959.0800
1306     880.8300
1313    2300.8700
1325    1600.2900
1327     879.9300
1341    1300.2400
1354    1199.6300
1381     921.5200
1696     951.5200
2225    1352.4200
2445    1050.7600
2448    1751.1800
2779     999.7400
2785     898.4000
3320    2560.2000
3326     917.1500
3366     934.9915
3387     934.1500
3463    2560.2000
3469     917.1500
3509     934.9915
3536     890.8000
3537    1054.4505
3542     918.0000
3552    1529.9915
3565    1163.6500
Name: new_price, dtype: float64

Removing Outliers from the DataFrame

# dropping these rows
df.drop(outlier_used_price.index, axis=0, inplace=True)

df.info()

<class 'pandas.core.frame.DataFrame'>
Int64Index: 3450 entries, 0 to 3570
Data columns (total 15 columns):
 #   Column            Non-Null Count  Dtype   
---  ------            --------------  -----   
 0   brand_name        3450 non-null   category
 1   os                3450 non-null   category
 2   screen_size       3450 non-null   float64 
 3   4g                3450 non-null   category
 4   5g                3450 non-null   category
 5   main_camera_mp    3296 non-null   float64 
 6   selfie_camera_mp  3450 non-null   float64 
 7   int_memory        3440 non-null   float64 
 8   ram               3440 non-null   float64 
 9   battery           3444 non-null   float64 
 10  weight            3443 non-null   float64 
 11  release_year      3450 non-null   int64   
 12  days_used         3450 non-null   int64   
 13  new_price         3450 non-null   float64 
 14  used_price        3450 non-null   float64 
dtypes: category(4), float64(9), int64(2)
memory usage: 338.7 KB

df.round({'new_price': 4})

	brand_name	os	screen_size	4g	5g	main_camera_mp	selfie_camera_mp	int_memory	ram	battery	weight	release_year	days_used	new_price	used_price
0	Honor	Android	23.97	yes	no	13.0	5.0	64.0	3.0	3020.0	146.0	2020	127	111.6200	86.96
1	Honor	Android	28.10	yes	yes	13.0	16.0	128.0	8.0	4300.0	213.0	2020	325	249.3900	161.49
2	Honor	Android	24.29	yes	yes	13.0	8.0	128.0	8.0	4200.0	213.0	2020	162	359.4700	268.55
3	Honor	Android	26.04	yes	yes	13.0	8.0	64.0	6.0	7250.0	480.0	2020	345	278.9300	180.23
4	Honor	Android	15.72	yes	no	13.0	8.0	64.0	3.0	5000.0	185.0	2020	293	140.8700	103.80
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
3561	Apple	iOS	11.27	yes	no	12.0	7.0	64.0	3.0	1821.0	148.0	2020	235	356.1500	263.75
3567	Asus	Android	15.24	yes	no	13.0	8.0	128.0	8.0	4000.0	200.0	2018	541	518.8145	259.30
3568	Alcatel	Android	18.73	yes	no	13.0	5.0	32.0	3.0	4000.0	165.0	2020	201	92.6500	69.81
3569	Alcatel	Android	18.73	yes	no	13.0	5.0	32.0	2.0	4000.0	160.0	2020	149	101.9150	76.07
3570	Alcatel	Android	13.49	yes	no	13.0	5.0	16.0	2.0	4000.0	168.0	2020	176	72.2415	50.48

3450 rows × 15 columns

df.info()

<class 'pandas.core.frame.DataFrame'>
Int64Index: 3450 entries, 0 to 3570
Data columns (total 15 columns):
 #   Column            Non-Null Count  Dtype   
---  ------            --------------  -----   
 0   brand_name        3450 non-null   category
 1   os                3450 non-null   category
 2   screen_size       3450 non-null   float64 
 3   4g                3450 non-null   category
 4   5g                3450 non-null   category
 5   main_camera_mp    3296 non-null   float64 
 6   selfie_camera_mp  3450 non-null   float64 
 7   int_memory        3440 non-null   float64 
 8   ram               3440 non-null   float64 
 9   battery           3444 non-null   float64 
 10  weight            3443 non-null   float64 
 11  release_year      3450 non-null   int64   
 12  days_used         3450 non-null   int64   
 13  new_price         3450 non-null   float64 
 14  used_price        3450 non-null   float64 
dtypes: category(4), float64(9), int64(2)
memory usage: 467.7 KB

Identifying Missing Values

df.isnull().sum().sort_values(ascending=False)

main_camera_mp      154
int_memory           10
ram                  10
weight                7
battery               6
brand_name            0
os                    0
screen_size           0
4g                    0
5g                    0
selfie_camera_mp      0
release_year          0
days_used             0
new_price             0
used_price            0
dtype: int64

Transforming Missing Values to the Median

df.median()

screen_size           13.490
main_camera_mp         8.000
selfie_camera_mp       5.000
int_memory            32.000
ram                    4.000
battery             3000.000
weight               158.000
release_year        2015.000
days_used            700.000
new_price            181.115
used_price            74.790
dtype: float64

df.fillna(df.median(), inplace=True)

df.isnull().sum().sort_values(ascending=False)

brand_name          0
os                  0
screen_size         0
4g                  0
5g                  0
main_camera_mp      0
selfie_camera_mp    0
int_memory          0
ram                 0
battery             0
weight              0
release_year        0
days_used           0
new_price           0
used_price          0
dtype: int64

Conducting Additional EDA

df_attr = df.iloc[:, 0:16]
sns.pairplot(df_attr, diag_kind='kde')

<seaborn.axisgrid.PairGrid at 0x2088b401760>

df.info()

<class 'pandas.core.frame.DataFrame'>
Int64Index: 3450 entries, 0 to 3570
Data columns (total 15 columns):
 #   Column            Non-Null Count  Dtype   
---  ------            --------------  -----   
 0   brand_name        3450 non-null   category
 1   os                3450 non-null   category
 2   screen_size       3450 non-null   float64 
 3   4g                3450 non-null   category
 4   5g                3450 non-null   category
 5   main_camera_mp    3450 non-null   float64 
 6   selfie_camera_mp  3450 non-null   float64 
 7   int_memory        3450 non-null   float64 
 8   ram               3450 non-null   float64 
 9   battery           3450 non-null   float64 
 10  weight            3450 non-null   float64 
 11  release_year      3450 non-null   int64   
 12  days_used         3450 non-null   int64   
 13  new_price         3450 non-null   float64 
 14  used_price        3450 non-null   float64 
dtypes: category(4), float64(9), int64(2)
memory usage: 467.7 KB

df.describe()

	screen_size	main_camera_mp	selfie_camera_mp	int_memory	ram	battery	weight	release_year	days_used	new_price	used_price
count	3450.000000	3450.000000	3450.000000	3450.000000	3450.000000	3450.000000	3450.000000	3450.000000	3450.000000	3450.000000	3450.000000
mean	14.621275	9.291287	6.256174	49.539309	3.962272	3023.475652	177.982304	2015.857391	687.591594	212.942016	93.062655
std	5.030298	4.706446	6.654136	74.744151	1.222456	1338.596984	89.235951	2.246987	242.317747	131.553900	69.530048
min	2.700000	0.080000	0.300000	0.005000	0.030000	80.000000	25.000000	2013.000000	91.000000	9.130000	2.510000
25%	11.430000	5.000000	2.000000	16.000000	4.000000	2070.000000	140.000000	2014.000000	554.000000	119.560000	44.940000
50%	13.490000	8.000000	5.000000	32.000000	4.000000	3000.000000	158.000000	2015.000000	700.000000	181.115000	74.790000
75%	16.030000	13.000000	8.000000	64.000000	4.000000	4000.000000	181.000000	2018.000000	878.000000	279.315000	120.040000
max	46.360000	48.000000	32.000000	1024.000000	16.000000	9600.000000	950.000000	2020.000000	1094.000000	921.520000	398.560000

plt.figure(figsize=(15, 7))
sns.heatmap(df.corr(), annot=True, vmin=-1, vmax=1, fmt=".2f", cmap="Spectral")
plt.show()

df.brand_name.value_counts()

Others        503
Samsung       347
Huawei        240
LG            199
Lenovo        172
ZTE           139
Xiaomi        130
Alcatel       125
Asus          122
Oppo          121
Nokia         120
Micromax      120
Honor         116
Vivo          112
HTC           109
Motorola      108
Sony           85
Meizu          60
Gionee         55
Acer           51
XOLO           49
Panasonic      47
Apple          43
Realme         41
Celkon         37
Lava           36
Karbonn        30
Spice          30
Microsoft      22
Coolpad        22
BlackBerry     22
OnePlus        14
Google         13
Infinix        10
Name: brand_name, dtype: int64

df.groupby(['brand_name']).mean()

	screen_size	main_camera_mp	selfie_camera_mp	int_memory	ram	battery	weight	release_year	days_used	new_price	used_price
brand_name
Acer	15.245490	6.967647	2.474510	23.215686	3.901961	2999.607843	225.872549	2014.372549	795.921569	172.867647	63.798431
Alcatel	13.128480	6.324800	2.260800	36.224000	3.426000	2393.360000	166.465600	2014.976000	752.632000	142.499092	55.326080
Apple	14.987907	9.837209	4.293023	34.604651	3.906977	3365.116279	194.002326	2016.069767	710.906977	495.803488	200.189767
Asus	15.453770	9.927459	4.337705	49.442623	4.000000	3368.778689	216.072951	2015.311475	757.081967	228.343725	89.766311
BlackBerry	12.410909	9.909091	5.140909	57.454545	3.829545	2822.500000	160.568182	2015.181818	692.909091	234.774545	102.039091
Celkon	9.554054	3.597297	0.635135	219.675676	1.466216	1459.459459	135.202703	2013.243243	801.405405	60.956486	22.648378
Coolpad	14.040000	10.818182	7.181818	36.363636	3.954545	2945.000000	154.381818	2016.363636	766.227273	194.285455	77.928182
Gionee	13.617091	9.857273	5.109091	42.181818	3.931818	3047.363636	160.085455	2014.909091	784.945455	239.120000	85.191818
Google	15.130000	11.892308	7.538462	56.615385	4.615385	3698.461538	191.076923	2017.923077	529.923077	408.600000	206.422308
HTC	12.945505	10.772477	5.697248	32.733945	4.000000	2606.330275	154.946789	2015.146789	760.238532	246.174679	96.653394
Honor	18.955690	12.327586	11.782759	71.517241	4.534483	3629.396552	177.272414	2018.129310	470.310345	229.032509	126.601552
Huawei	16.585625	10.181667	9.662500	62.866667	4.430458	3486.637500	196.465417	2016.975000	581.004167	240.924533	119.535083
Infinix	18.478000	8.000000	11.200000	38.400000	2.600000	4800.000000	184.400000	2019.600000	313.300000	106.017000	68.979000
Karbonn	11.683667	6.796667	1.823333	65.600333	3.375000	1730.000000	137.933333	2013.366667	820.066667	110.384333	38.069333
LG	13.535075	8.455528	4.602513	29.266332	3.736181	2830.050251	163.501759	2015.693467	691.266332	205.807452	89.054271
Lava	12.465278	6.909722	2.419444	104.000000	3.277778	2248.611111	140.408333	2014.527778	787.222222	107.424722	40.112778
Lenovo	16.110000	8.946221	5.158140	42.232558	3.886628	3653.255814	227.841279	2015.610465	724.767442	193.358779	77.147500
Meizu	15.188833	12.393333	10.316667	56.266667	4.333333	3312.083333	158.850000	2017.083333	672.266667	258.551833	116.346833
Micromax	12.176417	5.973750	2.271667	46.286667	3.750000	2225.416667	145.315000	2014.300000	816.508333	106.964667	38.134417
Microsoft	13.010000	9.454545	3.181818	31.272727	4.000000	2410.454545	172.795455	2014.863636	853.636364	166.366818	55.316818
Motorola	14.111389	12.148148	7.685185	48.444444	3.796296	3170.879630	164.042593	2017.055556	563.296296	191.120287	93.066759
Nokia	11.588250	5.581333	5.100000	44.601167	3.631250	2137.250000	136.257500	2016.308333	624.066667	126.524975	56.290500
OnePlus	18.460000	10.214286	13.285714	131.428571	5.142857	3456.785714	174.642857	2017.142857	642.500000	449.824857	213.767857
Oppo	15.485207	10.160744	14.328926	75.239669	4.727273	3335.702479	164.411157	2017.165289	569.388430	304.861686	153.208512
Others	13.854473	7.882167	3.874155	39.864940	3.732167	2796.182903	190.031412	2015.121272	745.011928	183.708203	73.482565
Panasonic	12.996170	10.324468	4.453191	27.914894	4.000000	2682.978723	149.103191	2015.574468	810.468085	171.426596	60.302979
Realme	17.655610	8.609756	11.365854	70.634146	4.195122	4337.317073	188.804878	2019.463415	313.390244	186.031415	124.169024
Samsung	14.302305	9.092075	5.546398	37.244957	3.974063	3145.351585	192.958501	2015.515850	722.847262	262.694536	108.180865
Sony	13.885765	14.258824	5.231765	30.870588	4.023529	2918.411765	177.504706	2015.211765	743.035294	257.420253	102.960118
Spice	11.746000	4.921667	1.573333	49.600000	3.750000	2191.000000	161.130000	2013.233333	881.233333	98.000000	32.299667
Vivo	18.663839	12.379464	14.056250	81.892857	4.611607	3687.276786	171.541518	2017.803571	512.098214	306.192366	155.356696
XOLO	12.482041	7.455102	1.718367	22.204082	4.000000	2220.000000	152.016327	2013.653061	823.244898	130.898571	47.340204
Xiaomi	18.828923	11.657692	11.776154	73.169231	4.461538	3919.076923	182.635385	2017.615385	548.192308	231.294904	121.526231
ZTE	13.818201	11.364029	6.263309	43.741007	3.965827	2846.582734	155.595324	2015.856115	732.640288	209.717266	87.906115

df.groupby(['os']).mean()

	screen_size	main_camera_mp	selfie_camera_mp	int_memory	ram	battery	weight	release_year	days_used	new_price	used_price
os
Android	15.142748	9.640051	6.553868	49.219487	4.028494	3141.343840	182.612830	2015.941102	683.105062	217.486410	95.773989
Others	7.092500	3.828700	3.291500	64.521025	2.916700	1409.785000	109.077750	2015.085000	700.945000	88.638058	37.493250
Windows	12.578657	8.877612	2.334328	29.134328	4.000000	2182.089552	160.856716	2014.149254	837.507463	191.430448	65.083433
iOS	14.732381	9.880952	4.366667	34.666667	3.928571	3235.071429	187.121429	2016.000000	720.380952	499.325952	199.543333

df.groupby(['os']).describe()

	screen_size								main_camera_mp								selfie_camera_mp								int_memory								ram								battery								weight								release_year								days_used								new_price								used_price
	count	mean	std	min	25%	50%	75%	max	count	mean	std	min	25%	50%	75%	max	count	mean	std	min	25%	50%	75%	max	count	mean	std	min	25%	50%	75%	max	count	mean	std	min	25%	50%	75%	max	count	mean	std	min	25%	50%	75%	max	count	mean	std	min	25%	50%	75%	max	count	mean	std	min	25%	50%	75%	max	count	mean	std	min	25%	50%	75%	max	count	mean	std	min	25%	50%	75%	max	count	mean	std	min	25%	50%	75%	max
os
Android	3141.0	15.142748	4.693865	2.86	12.70	13.49	16.67	46.36	3141.0	9.640051	4.512623	0.30	5.0	8.0	13.0	48.0	3141.0	6.553868	6.817000	0.3	2.0	5.0	8.0	32.0	3141.0	49.219487	74.238612	0.010	16.0	32.0	64.0	1024.0	3141.0	4.028494	1.062303	0.25	4.00	4.0	4.0	12.0	3141.0	3141.343840	1266.632676	225.0	2200.0	3000.0	4000.00	9600.0	3141.0	182.612830	87.669245	46.0	143.000	160.0	183.600	950.0	3141.0	2015.941102	2.242333	2013.0	2014.0	2016.0	2018.0	2020.0	3141.0	683.105062	243.842462	91.0	548.00	696.0	875.00	1094.0	3141.0	217.486410	125.212456	30.81	121.9200	189.81	279.7800	921.52	3141.0	95.773989	68.522442	9.30	47.9400	75.580	120.8400	398.56
Others	200.0	7.092500	3.877846	2.70	5.40	5.72	8.41	31.27	200.0	3.828700	3.927516	0.08	0.3	2.0	5.0	13.0	200.0	3.291500	3.892020	0.3	0.3	2.0	5.0	20.0	200.0	64.521025	96.757882	0.005	16.0	32.0	64.0	512.0	200.0	2.916700	2.627060	0.03	0.25	4.0	4.0	16.0	200.0	1409.785000	980.947772	80.0	820.0	1200.0	1830.00	8827.0	200.0	109.077750	60.185698	25.0	77.375	98.1	136.250	544.3	200.0	2015.085000	2.344195	2013.0	2013.0	2014.0	2017.0	2020.0	200.0	700.945000	233.046854	117.0	568.25	703.5	883.25	1094.0	200.0	88.638058	87.656717	9.13	21.6075	54.97	122.9750	430.09	200.0	37.493250	41.217811	2.51	9.5350	20.555	47.5275	227.34
Windows	67.0	12.578657	3.610521	10.16	10.16	11.27	12.70	27.94	67.0	8.877612	6.489101	2.00	5.0	6.7	8.0	41.0	67.0	2.334328	1.996156	0.3	1.0	1.6	5.0	8.0	67.0	29.134328	7.841026	16.000	32.0	32.0	32.0	64.0	67.0	4.000000	0.000000	4.00	4.00	4.0	4.0	4.0	67.0	2182.089552	613.774431	1200.0	1800.0	2000.0	2500.00	4150.0	67.0	160.856716	88.400727	98.9	134.000	146.0	159.500	675.9	67.0	2014.149254	0.821192	2013.0	2014.0	2014.0	2015.0	2016.0	67.0	837.507463	147.439805	564.0	706.50	824.0	953.50	1089.0	67.0	191.430448	121.202627	59.72	99.4850	159.92	269.2350	699.46	67.0	65.083433	42.204799	17.82	32.6150	55.300	91.4500	279.97
iOS	42.0	14.732381	6.566622	3.33	11.27	13.49	19.21	27.94	42.0	9.880952	2.370576	5.00	8.0	12.0	12.0	12.0	42.0	4.366667	2.698840	1.2	1.2	6.0	7.0	7.0	42.0	34.666667	17.990060	16.000	16.0	32.0	32.0	64.0	42.0	3.928571	0.341650	2.00	4.00	4.0	4.0	4.0	42.0	3235.071429	2759.796930	205.0	334.0	2720.5	5400.75	8827.0	42.0	187.121429	160.348397	25.0	43.375	140.5	300.125	469.0	42.0	2016.000000	1.912730	2013.0	2014.0	2016.0	2017.0	2020.0	42.0	720.380952	216.616662	235.0	592.75	702.0	868.50	1082.0	42.0	499.325952	180.177720	247.70	357.1200	450.07	689.1125	879.72	42.0	199.543333	86.340442	81.21	124.4025	193.590	275.5525	375.23

Transforming Categorical Data to Dummy Variables

df = pd.get_dummies(df, columns=['brand_name','os','4g','5g'])
df.head()

	screen_size	main_camera_mp	selfie_camera_mp	int_memory	ram	battery	weight	release_year	days_used	new_price	used_price	brand_name_Acer	brand_name_Alcatel	brand_name_Apple	brand_name_Asus	brand_name_BlackBerry	brand_name_Celkon	brand_name_Coolpad	brand_name_Gionee	brand_name_Google	brand_name_HTC	brand_name_Honor	brand_name_Huawei	brand_name_Infinix	brand_name_Karbonn	brand_name_LG	brand_name_Lava	brand_name_Lenovo	brand_name_Meizu	brand_name_Micromax	brand_name_Microsoft	brand_name_Motorola	brand_name_Nokia	brand_name_OnePlus	brand_name_Oppo	brand_name_Others	brand_name_Panasonic	brand_name_Realme	brand_name_Samsung	brand_name_Sony	brand_name_Spice	brand_name_Vivo	brand_name_XOLO	brand_name_Xiaomi	brand_name_ZTE	os_Android	os_Others	os_Windows	os_iOS	4g_no	4g_yes	5g_no	5g_yes
0	23.97	13.0	5.0	64.0	3.0	3020.0	146.0	2020	127	111.62	86.96	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	1	1	0
1	28.10	13.0	16.0	128.0	8.0	4300.0	213.0	2020	325	249.39	161.49	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	1	0	1
2	24.29	13.0	8.0	128.0	8.0	4200.0	213.0	2020	162	359.47	268.55	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	1	0	1
3	26.04	13.0	8.0	64.0	6.0	7250.0	480.0	2020	345	278.93	180.23	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	1	0	1
4	15.72	13.0	8.0	64.0	3.0	5000.0	185.0	2020	293	140.87	103.80	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	1	1	0

Loading more libraries

from sklearn.model_selection import train_test_split
from sklearn.linear_model import LinearRegression
from sklearn.metrics import mean_squared_error

Splitting the Data Set

X = df.drop("used_price", axis=1)
y = df["used_price"]

# splitting the data in 70:30 ratio for train to test data

X_train, X_test, y_train, y_test = train_test_split(
    X, y, test_size=0.30, random_state=1
)

X_train.describe()

	screen_size	main_camera_mp	selfie_camera_mp	int_memory	ram	battery	weight	release_year	days_used	new_price	brand_name_Acer	brand_name_Alcatel	brand_name_Apple	brand_name_Asus	brand_name_BlackBerry	brand_name_Celkon	brand_name_Coolpad	brand_name_Gionee	brand_name_Google	brand_name_HTC	brand_name_Honor	brand_name_Huawei	brand_name_Infinix	brand_name_Karbonn	brand_name_LG	brand_name_Lava	brand_name_Lenovo	brand_name_Meizu	brand_name_Micromax	brand_name_Microsoft	brand_name_Motorola	brand_name_Nokia	brand_name_OnePlus	brand_name_Oppo	brand_name_Others	brand_name_Panasonic	brand_name_Realme	brand_name_Samsung	brand_name_Sony	brand_name_Spice	brand_name_Vivo	brand_name_XOLO	brand_name_Xiaomi	brand_name_ZTE	os_Android	os_Others	os_Windows	os_iOS	4g_no	4g_yes	5g_no	5g_yes
count	2415.000000	2415.000000	2415.000000	2415.000000	2415.000000	2415.000000	2415.000000	2415.000000	2415.000000	2415.000000	2415.000000	2415.000000	2415.000000	2415.000000	2415.000000	2415.000000	2415.000000	2415.000000	2415.000000	2415.000000	2415.000000	2415.000000	2415.000000	2415.000000	2415.000000	2415.000000	2415.000000	2415.000000	2415.000000	2415.000000	2415.000000	2415.000000	2415.000000	2415.000000	2415.000000	2415.000000	2415.000000	2415.000000	2415.000000	2415.000000	2415.000000	2415.000000	2415.000000	2415.000000	2415.000000	2415.000000	2415.000000	2415.000000	2415.000000	2415.000000	2415.000000	2415.000000
mean	14.739665	9.426969	6.435735	49.265863	3.975400	3044.078675	178.561387	2015.919669	682.623188	215.519618	0.014907	0.037681	0.013665	0.034783	0.006625	0.008282	0.007039	0.013665	0.002070	0.030228	0.032298	0.072050	0.002899	0.009524	0.057143	0.009524	0.050932	0.016977	0.034369	0.005383	0.033126	0.035197	0.004969	0.038509	0.136232	0.015321	0.012836	0.102277	0.024845	0.009110	0.035611	0.016149	0.034783	0.040994	0.912629	0.056315	0.017391	0.013665	0.338302	0.661698	0.972257	0.027743
std	5.035455	4.677233	6.689711	73.301312	1.240719	1315.422892	88.403798	2.252350	242.781953	132.420552	0.121205	0.190463	0.116118	0.183267	0.081142	0.090644	0.083622	0.116118	0.045464	0.171249	0.176827	0.258624	0.053771	0.097144	0.232163	0.097144	0.219904	0.129213	0.182212	0.073186	0.179003	0.184315	0.070330	0.192462	0.343106	0.122851	0.112592	0.303076	0.155684	0.095029	0.185356	0.126075	0.183267	0.198317	0.282436	0.230576	0.130751	0.116118	0.473230	0.473230	0.164270	0.164270
min	2.860000	0.080000	0.300000	0.005000	0.030000	80.000000	25.000000	2013.000000	92.000000	9.130000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000
25%	12.700000	5.000000	2.000000	16.000000	4.000000	2100.000000	140.000000	2014.000000	547.000000	120.030000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	1.000000	0.000000	0.000000	0.000000	0.000000	0.000000	1.000000	0.000000
50%	13.490000	8.000000	5.000000	32.000000	4.000000	3000.000000	159.000000	2015.000000	696.000000	183.320000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	1.000000	0.000000	0.000000	0.000000	0.000000	1.000000	1.000000	0.000000
75%	16.030000	13.000000	8.000000	64.000000	4.000000	4000.000000	182.000000	2018.000000	874.000000	280.195000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	1.000000	0.000000	0.000000	0.000000	1.000000	1.000000	1.000000	0.000000
max	46.360000	48.000000	32.000000	1024.000000	16.000000	9600.000000	950.000000	2020.000000	1094.000000	921.520000	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000

Model Building

Fitting the model to the training set

# intialize the model to be fit and fit the model on the train data

regression_model = LinearRegression()
regression_model.fit(X_train, y_train)

LinearRegression()

Get the score on training set

# get the score (R-squared) on the training set

print(
    "The score (R-squared) on the training set is ",
    regression_model.score(X_train, y_train),
)

The score (R-squared) on the training set is  0.9452839434052618

def r_squared(model, X, y):
    y_mean = y.mean()
    SST = ((y - y_mean) ** 2).sum()
    SSE = ((y - model.predict(X)) ** 2).sum()
    r_square = 1 - SSE / SST
    return SSE, SST, r_square


SSE, SST, r_square = r_squared(regression_model, X_train, y_train)
print("SSE: ", SSE)
print("SST: ", SST)
print("R-squared: ", r_square)

SSE:  649120.7141178057
SST:  11863441.090530433
R-squared:  0.9452839434052618

Get the score on test set

# get the score (R-squared) on the test set

print(
    "The score (R-squared) on the test set is ", regression_model.score(X_test, y_test)
)

The score (R-squared) on the test set is  0.9367482592294135

Get the RMSE on train set

print(
    "The Root Mean Square Error (RMSE) of the model for the training set is ",
    np.sqrt(mean_squared_error(y_train, regression_model.predict(X_train))),
)

The Root Mean Square Error (RMSE) of the model for the training set is  16.394726139321644

Get the RMSE on test set

print(
    "The Root Mean Square Error (RMSE) of the model for the test set is ",
    np.sqrt(mean_squared_error(y_test, regression_model.predict(X_test))),
)

The Root Mean Square Error (RMSE) of the model for the test set is  17.119211146538838

Get the model coefficients

# let's check the coefficients and intercept of the model

coef_df = pd.DataFrame(
    np.append(regression_model.coef_, regression_model.intercept_),
    index=X_train.columns.tolist() + ["Intercept"],
    columns=["Coefficients"],
)

coef_df

	Coefficients
screen_size	0.053543
main_camera_mp	-0.805988
selfie_camera_mp	0.613928
int_memory	0.035250
ram	2.804793
battery	-0.000369
weight	-0.007774
release_year	0.847579
days_used	-0.095390
new_price	0.421928
brand_name_Acer	0.176839
brand_name_Alcatel	0.114099
brand_name_Apple	-3.611314
brand_name_Asus	0.086774
brand_name_BlackBerry	5.661039
brand_name_Celkon	4.932113
brand_name_Coolpad	-0.895105
brand_name_Gionee	-6.186673
brand_name_Google	38.919759
brand_name_HTC	-0.472049
brand_name_Honor	-4.761710
brand_name_Huawei	-2.382855
brand_name_Infinix	-16.731424
brand_name_Karbonn	2.400784
brand_name_LG	1.391148
brand_name_Lava	1.182560
brand_name_Lenovo	-3.950064
brand_name_Meizu	-1.038285
brand_name_Micromax	1.549807
brand_name_Microsoft	-0.705211
brand_name_Motorola	-2.171833
brand_name_Nokia	-8.527877
brand_name_OnePlus	6.782538
brand_name_Oppo	-5.523624
brand_name_Others	-0.101932
brand_name_Panasonic	-1.468594
brand_name_Realme	-8.524781
brand_name_Samsung	-1.486388
brand_name_Sony	2.117931
brand_name_Spice	6.432004
brand_name_Vivo	-3.842789
brand_name_XOLO	1.990760
brand_name_Xiaomi	-2.427485
brand_name_ZTE	1.071837
os_Android	1.118320
os_Others	-0.915887
os_Windows	3.408881
os_iOS	-3.611314
4g_no	1.854243
4g_yes	-1.854243
5g_no	-23.191041
5g_yes	23.191041
Intercept	-1624.738093

Automate the equation of the fit

# Let us write the equation of linear regression

Equation = "Price = " + str(regression_model.intercept_)
print(Equation, end=" ")

for i in range(len(X_train.columns)):
    if i != len(X_train.columns) - 1:
        print(
            "+ (",
            regression_model.coef_[i],
            ")*(",
            X_train.columns[i],
            ")",
            end="  ",
        )
    else:
        print("+ (", regression_model.coef_[i], ")*(", X_train.columns[i], ")")

Price = -1624.7380934470625 + ( 0.053543257233632964 )*( screen_size )  + ( -0.8059880670283929 )*( main_camera_mp )  + ( 0.6139278221200691 )*( selfie_camera_mp )  + ( 0.035250008079695194 )*( int_memory )  + ( 2.8047927240222434 )*( ram )  + ( -0.00036886250308776347 )*( battery )  + ( -0.007773780146768772 )*( weight )  + ( 0.8475793211476059 )*( release_year )  + ( -0.09539020733014647 )*( days_used )  + ( 0.42192819655928737 )*( new_price )  + ( 0.17683870408045266 )*( brand_name_Acer )  + ( 0.11409920144222552 )*( brand_name_Alcatel )  + ( -3.611314225928028 )*( brand_name_Apple )  + ( 0.08677380329715056 )*( brand_name_Asus )  + ( 5.661038962081446 )*( brand_name_BlackBerry )  + ( 4.932112901893202 )*( brand_name_Celkon )  + ( -0.8951047730223278 )*( brand_name_Coolpad )  + ( -6.186673023060855 )*( brand_name_Gionee )  + ( 38.91975923037877 )*( brand_name_Google )  + ( -0.4720491164182672 )*( brand_name_HTC )  + ( -4.7617104438507285 )*( brand_name_Honor )  + ( -2.3828550916040747 )*( brand_name_Huawei )  + ( -16.73142429585952 )*( brand_name_Infinix )  + ( 2.400784090794901 )*( brand_name_Karbonn )  + ( 1.3911476829752747 )*( brand_name_LG )  + ( 1.1825602038011374 )*( brand_name_Lava )  + ( -3.9500638709963978 )*( brand_name_Lenovo )  + ( -1.0382852126359072 )*( brand_name_Meizu )  + ( 1.549807013143882 )*( brand_name_Micromax )  + ( -0.7052107172917577 )*( brand_name_Microsoft )  + ( -2.1718328954287993 )*( brand_name_Motorola )  + ( -8.527877119398536 )*( brand_name_Nokia )  + ( 6.782538413228437 )*( brand_name_OnePlus )  + ( -5.523623518801358 )*( brand_name_Oppo )  + ( -0.10193153821370382 )*( brand_name_Others )  + ( -1.4685938547421555 )*( brand_name_Panasonic )  + ( -8.524781297587573 )*( brand_name_Realme )  + ( -1.4863879512396525 )*( brand_name_Samsung )  + ( 2.1179308231072813 )*( brand_name_Sony )  + ( 6.4320040767325235 )*( brand_name_Spice )  + ( -3.842788929304269 )*( brand_name_Vivo )  + ( 1.9907604163679307 )*( brand_name_XOLO )  + ( -2.4274846546746947 )*( brand_name_Xiaomi )  + ( 1.0718370067356204 )*( brand_name_ZTE )  + ( 1.1183201070051179 )*( os_Android )  + ( -0.915886693708293 )*( os_Others )  + ( 3.4088808126179195 )*( os_Windows )  + ( -3.6113142259284348 )*( os_iOS )  + ( 1.854242784269469 )*( 4g_no )  + ( -1.8542427842662619 )*( 4g_yes )  + ( -23.19104135493962 )*( 5g_no )  + ( 23.191041354939664 )*( 5g_yes )

Model Building (statsmodels)

import statsmodels.api as sm

# this adds the constant term to the dataset
X_con = sm.add_constant(X)

X_trainc, X_testc, y_trainc, y_testc = train_test_split(
    X_con, y, test_size=0.30, random_state=1
)

Make the linear model using statsmodels OLS and print the model summary.

model = sm.OLS(y_trainc, X_trainc).fit()
model.summary()

OLS Regression Results

Dep. Variable:	used_price	R-squared:	0.945
Model:	OLS	Adj. R-squared:	0.944
Method:	Least Squares	F-statistic:	870.1
Date:	Wed, 29 Sep 2021	Prob (F-statistic):	0.00
Time:	23:56:28	Log-Likelihood:	-10181.
No. Observations:	2415	AIC:	2.046e+04
Df Residuals:	2367	BIC:	2.074e+04
Df Model:	47
Covariance Type:	nonrobust

	coef	std err	t	P>|t|	[0.025	0.975]
const	-704.0532	273.335	-2.576	0.010	-1240.054	-168.052
screen_size	0.0535	0.120	0.445	0.657	-0.183	0.290
main_camera_mp	-0.8060	0.104	-7.776	0.000	-1.009	-0.603
selfie_camera_mp	0.6139	0.086	7.142	0.000	0.445	0.782
int_memory	0.0353	0.005	6.743	0.000	0.025	0.046
ram	2.8048	0.346	8.108	0.000	2.126	3.483
battery	-0.0004	0.001	-0.717	0.474	-0.001	0.001
weight	-0.0078	0.007	-1.067	0.286	-0.022	0.007
release_year	0.8476	0.313	2.711	0.007	0.234	1.461
days_used	-0.0954	0.002	-43.717	0.000	-0.100	-0.091
new_price	0.4219	0.004	110.565	0.000	0.414	0.429
brand_name_Acer	-17.8758	7.471	-2.393	0.017	-32.527	-3.225
brand_name_Alcatel	-17.9385	7.230	-2.481	0.013	-32.116	-3.761
brand_name_Apple	-111.9272	42.197	-2.653	0.008	-194.674	-29.181
brand_name_Asus	-17.9659	7.216	-2.490	0.013	-32.116	-3.816
brand_name_BlackBerry	-12.3916	7.843	-1.580	0.114	-27.772	2.989
brand_name_Celkon	-13.1205	7.682	-1.708	0.088	-28.184	1.943
brand_name_Coolpad	-18.9478	8.099	-2.340	0.019	-34.829	-3.067
brand_name_Gionee	-24.2393	7.470	-3.245	0.001	-38.889	-9.590
brand_name_Google	20.8671	10.344	2.017	0.044	0.583	41.152
brand_name_HTC	-18.5247	7.177	-2.581	0.010	-32.598	-4.452
brand_name_Honor	-22.8144	7.344	-3.107	0.002	-37.216	-8.413
brand_name_Huawei	-20.4355	7.200	-2.838	0.005	-34.555	-6.316
brand_name_Infinix	-34.7841	9.428	-3.690	0.000	-53.272	-16.297
brand_name_Karbonn	-15.6519	7.651	-2.046	0.041	-30.656	-0.648
brand_name_LG	-16.6615	7.141	-2.333	0.020	-30.665	-2.658
brand_name_Lava	-16.8701	7.854	-2.148	0.032	-32.272	-1.468
brand_name_Lenovo	-22.0027	7.170	-3.069	0.002	-36.062	-7.943
brand_name_Meizu	-19.0909	7.595	-2.514	0.012	-33.985	-4.197
brand_name_Micromax	-16.5028	7.250	-2.276	0.023	-30.719	-2.287
brand_name_Microsoft	-18.7579	9.167	-2.046	0.041	-36.733	-0.782
brand_name_Motorola	-20.2245	7.360	-2.748	0.006	-34.657	-5.792
brand_name_Nokia	-26.5805	7.439	-3.573	0.000	-41.169	-11.992
brand_name_OnePlus	-11.2701	8.551	-1.318	0.188	-28.039	5.499
brand_name_Oppo	-23.5763	7.205	-3.272	0.001	-37.705	-9.447
brand_name_Others	-18.1546	7.117	-2.551	0.011	-32.110	-4.199
brand_name_Panasonic	-19.5212	7.588	-2.573	0.010	-34.401	-4.641
brand_name_Realme	-26.5774	7.831	-3.394	0.001	-41.935	-11.220
brand_name_Samsung	-19.5390	7.072	-2.763	0.006	-33.407	-5.671
brand_name_Sony	-15.9347	7.209	-2.210	0.027	-30.072	-1.797
brand_name_Spice	-11.6206	7.714	-1.506	0.132	-26.747	3.506
brand_name_Vivo	-21.8954	7.248	-3.021	0.003	-36.108	-7.683
brand_name_XOLO	-16.0619	7.400	-2.171	0.030	-30.572	-1.552
brand_name_Xiaomi	-20.4801	7.224	-2.835	0.005	-34.646	-6.315
brand_name_ZTE	-16.9808	7.182	-2.364	0.018	-31.065	-2.896
os_Android	-197.4608	77.072	-2.562	0.010	-348.597	-46.324
os_Others	-199.4950	77.258	-2.582	0.010	-350.995	-47.995
os_Windows	-195.1702	76.895	-2.538	0.011	-345.959	-44.381
os_iOS	-111.9272	42.197	-2.653	0.008	-194.674	-29.181
4g_no	-350.1723	136.481	-2.566	0.010	-617.807	-82.538
4g_yes	-353.8808	136.856	-2.586	0.010	-622.251	-85.511
5g_no	-375.2176	136.587	-2.747	0.006	-643.060	-107.375
5g_yes	-328.8355	136.759	-2.404	0.016	-597.016	-60.655

Omnibus:	464.933	Durbin-Watson:	1.979
Prob(Omnibus):	0.000	Jarque-Bera (JB):	4106.540
Skew:	0.650	Prob(JB):	0.00
Kurtosis:	9.255	Cond. No.	1.04e+16

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The smallest eigenvalue is 3.35e-22. This might indicate that there are
strong multicollinearity problems or that the design matrix is singular.

Get the value of the coefficient of determination.

print("The coefficient of determination (R-squared) is ", model.rsquared)

The coefficient of determination (R-squared) is  0.9452839434052618

Automate the equation of fit

# Let us write the equation of linear regression
Equation = "Price ="
print(Equation, end=" ")
for i in range(len(X_trainc.columns)):
    if i == 0:
        print(model.params[i], "+", end=" ")
    elif i != len(X_trainc.columns) - 1:
        print(
            "(",
            model.params[i],
            ")*(",
            X_trainc.columns[i],
            ")",
            "+",
            end="  ",
        )
    else:
        print("(", model.params[i], ")*(", X_trainc.columns[i], ")")

Price = -704.0531737377777 + ( 0.053543257239236475 )*( selfie_camera_mp ) +  ( -0.8059880670267164 )*( int_memory ) +  ( 0.6139278221304648 )*( ram ) +  ( 0.03525000807973884 )*( release_year ) +  ( 2.804792724014244 )*( days_used ) +  ( -0.00036886250306190026 )*( new_price ) +  ( -0.007773780147057652 )*( used_price ) +  ( 0.8475793210455903 )*( brand_name_Acer ) +  ( -0.09539020733050882 )*( brand_name_Alcatel ) +  ( 0.4219281965590277 )*( brand_name_Apple ) +  ( -17.87580677639521 )*( brand_name_Asus ) +  ( -17.938546279024962 )*( brand_name_BlackBerry ) +  ( -111.92718710861979 )*( brand_name_Celkon ) +  ( -17.965871677170913 )*( brand_name_Coolpad ) +  ( -12.391606518485354 )*( brand_name_Gionee ) +  ( -13.12053257869044 )*( brand_name_HTC ) +  ( -18.947750253461447 )*( brand_name_Honor ) +  ( -24.23931850354949 )*( brand_name_Huawei ) +  ( 20.867113750086492 )*( brand_name_Infinix ) +  ( -18.52469459690521 )*( brand_name_Karbonn ) +  ( -22.814355924283312 )*( brand_name_LG ) +  ( -20.435500572040812 )*( brand_name_Lava ) +  ( -34.784069776286586 )*( brand_name_Lenovo ) +  ( -15.651861389722239 )*( brand_name_Meizu ) +  ( -16.66149779749055 )*( brand_name_Micromax ) +  ( -16.870085276632167 )*( brand_name_Microsoft ) +  ( -22.002709351459313 )*( brand_name_Motorola ) +  ( -19.090930693058638 )*( brand_name_Nokia ) +  ( -16.502838467313005 )*( brand_name_Oppo ) +  ( -18.757856197639022 )*( brand_name_Others ) +  ( -20.224478375858393 )*( brand_name_Panasonic ) +  ( -26.580522599802514 )*( brand_name_Realme ) +  ( -11.270107067227393 )*( brand_name_Samsung ) +  ( -23.576268999273246 )*( brand_name_Sony ) +  ( -18.154577018661403 )*( brand_name_Vivo ) +  ( -19.521239335173487 )*( brand_name_Xiaomi ) +  ( -26.57742677796724 )*( brand_name_ZTE ) +  ( -19.53903343170927 )*( os_Android ) +  ( -15.934714657404236 )*( os_Others ) +  ( -11.620641403789392 )*( os_Windows ) +  ( -21.895434409766995 )*( os_iOS ) +  ( -16.061885064125164 )*( 4g_no ) +  ( -20.480130135145345 )*( 4g_yes ) +  ( -16.980808473725084 )*( 5g_no ) +  ( -197.4607801779984 )*( 5g_yes )

X_trainc.info()

<class 'pandas.core.frame.DataFrame'>
Int64Index: 3450 entries, 0 to 3570
Data columns (total 46 columns):
 #   Column                 Non-Null Count  Dtype  
---  ------                 --------------  -----  
 0   main_camera_mp         3450 non-null   float64
 1   selfie_camera_mp       3450 non-null   float64
 2   int_memory             3450 non-null   float64
 3   ram                    3450 non-null   float64
 4   release_year           3450 non-null   int64  
 5   days_used              3450 non-null   int64  
 6   new_price              3450 non-null   float64
 7   used_price             3450 non-null   float64
 8   brand_name_Acer        3450 non-null   uint8  
 9   brand_name_Alcatel     3450 non-null   uint8  
 10  brand_name_Apple       3450 non-null   uint8  
 11  brand_name_Asus        3450 non-null   uint8  
 12  brand_name_BlackBerry  3450 non-null   uint8  
 13  brand_name_Celkon      3450 non-null   uint8  
 14  brand_name_Coolpad     3450 non-null   uint8  
 15  brand_name_Gionee      3450 non-null   uint8  
 16  brand_name_HTC         3450 non-null   uint8  
 17  brand_name_Honor       3450 non-null   uint8  
 18  brand_name_Huawei      3450 non-null   uint8  
 19  brand_name_Infinix     3450 non-null   uint8  
 20  brand_name_Karbonn     3450 non-null   uint8  
 21  brand_name_LG          3450 non-null   uint8  
 22  brand_name_Lava        3450 non-null   uint8  
 23  brand_name_Lenovo      3450 non-null   uint8  
 24  brand_name_Meizu       3450 non-null   uint8  
 25  brand_name_Micromax    3450 non-null   uint8  
 26  brand_name_Microsoft   3450 non-null   uint8  
 27  brand_name_Motorola    3450 non-null   uint8  
 28  brand_name_Nokia       3450 non-null   uint8  
 29  brand_name_Oppo        3450 non-null   uint8  
 30  brand_name_Others      3450 non-null   uint8  
 31  brand_name_Panasonic   3450 non-null   uint8  
 32  brand_name_Realme      3450 non-null   uint8  
 33  brand_name_Samsung     3450 non-null   uint8  
 34  brand_name_Sony        3450 non-null   uint8  
 35  brand_name_Vivo        3450 non-null   uint8  
 36  brand_name_Xiaomi      3450 non-null   uint8  
 37  brand_name_ZTE         3450 non-null   uint8  
 38  os_Android             3450 non-null   uint8  
 39  os_Others              3450 non-null   uint8  
 40  os_Windows             3450 non-null   uint8  
 41  os_iOS                 3450 non-null   uint8  
 42  4g_no                  3450 non-null   uint8  
 43  4g_yes                 3450 non-null   uint8  
 44  5g_no                  3450 non-null   uint8  
 45  5g_yes                 3450 non-null   uint8  
dtypes: float64(6), int64(2), uint8(38)
memory usage: 499.6 KB

X_testc.info()

<class 'pandas.core.frame.DataFrame'>
Int64Index: 1035 entries, 1473 to 3084
Data columns (total 53 columns):
 #   Column                 Non-Null Count  Dtype  
---  ------                 --------------  -----  
 0   const                  1035 non-null   float64
 1   screen_size            1035 non-null   float64
 2   main_camera_mp         1035 non-null   float64
 3   selfie_camera_mp       1035 non-null   float64
 4   int_memory             1035 non-null   float64
 5   ram                    1035 non-null   float64
 6   battery                1035 non-null   float64
 7   weight                 1035 non-null   float64
 8   release_year           1035 non-null   int64  
 9   days_used              1035 non-null   int64  
 10  new_price              1035 non-null   float64
 11  brand_name_Acer        1035 non-null   uint8  
 12  brand_name_Alcatel     1035 non-null   uint8  
 13  brand_name_Apple       1035 non-null   uint8  
 14  brand_name_Asus        1035 non-null   uint8  
 15  brand_name_BlackBerry  1035 non-null   uint8  
 16  brand_name_Celkon      1035 non-null   uint8  
 17  brand_name_Coolpad     1035 non-null   uint8  
 18  brand_name_Gionee      1035 non-null   uint8  
 19  brand_name_Google      1035 non-null   uint8  
 20  brand_name_HTC         1035 non-null   uint8  
 21  brand_name_Honor       1035 non-null   uint8  
 22  brand_name_Huawei      1035 non-null   uint8  
 23  brand_name_Infinix     1035 non-null   uint8  
 24  brand_name_Karbonn     1035 non-null   uint8  
 25  brand_name_LG          1035 non-null   uint8  
 26  brand_name_Lava        1035 non-null   uint8  
 27  brand_name_Lenovo      1035 non-null   uint8  
 28  brand_name_Meizu       1035 non-null   uint8  
 29  brand_name_Micromax    1035 non-null   uint8  
 30  brand_name_Microsoft   1035 non-null   uint8  
 31  brand_name_Motorola    1035 non-null   uint8  
 32  brand_name_Nokia       1035 non-null   uint8  
 33  brand_name_OnePlus     1035 non-null   uint8  
 34  brand_name_Oppo        1035 non-null   uint8  
 35  brand_name_Others      1035 non-null   uint8  
 36  brand_name_Panasonic   1035 non-null   uint8  
 37  brand_name_Realme      1035 non-null   uint8  
 38  brand_name_Samsung     1035 non-null   uint8  
 39  brand_name_Sony        1035 non-null   uint8  
 40  brand_name_Spice       1035 non-null   uint8  
 41  brand_name_Vivo        1035 non-null   uint8  
 42  brand_name_XOLO        1035 non-null   uint8  
 43  brand_name_Xiaomi      1035 non-null   uint8  
 44  brand_name_ZTE         1035 non-null   uint8  
 45  os_Android             1035 non-null   uint8  
 46  os_Others              1035 non-null   uint8  
 47  os_Windows             1035 non-null   uint8  
 48  os_iOS                 1035 non-null   uint8  
 49  4g_no                  1035 non-null   uint8  
 50  4g_yes                 1035 non-null   uint8  
 51  5g_no                  1035 non-null   uint8  
 52  5g_yes                 1035 non-null   uint8  
dtypes: float64(9), int64(2), uint8(42)
memory usage: 139.5 KB

7 Variables: screen size, battery, weight, Google brand, OnePlus brand, Splice brand, and XOLO brand affected the regression line of best fit dramatically. Including these variables cause the prediction of price to be less accurate based on the dataset provided.